Ch 2.4, Ch 8.2 The scalar $\langle\phi|\psi\rangle = \int\phi^*(x)\psi(x)\,dx$ (position representation) or $\langle\phi|\psi\rangle = \sum_n \langle\phi|n\rangle\langle n|\psi\rangle$ (discrete basis). The inner product defines probability amplitudes, orthogonality, and normalization. *See also:* B